Which measurements could create more than one triangle? Explain how you found your answer and show your work.
A.
A triangle with sides measuring 6 inches, 8 inches, and 10 inches

B.
A triangle with sides measuring 5 cm and 10 cm and an included angle measuring 40°
C.
A triangle with angles measuring 75°, 60°, and 45°

D.
A triangle with sides measuring 4 inches, 8 inches, and 15 inches
All of the measurements could create more than one triangle. To find this answer, we can use the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the measure of the third side.
A. 6 + 8 > 10, 8 + 10 > 6, 6 + 10 > 8
B. 5 + 10 > 40°, 10 + 40° > 5, 5 + 40° > 10
C. 75° + 60° > 45°, 60° + 45° > 75°, 75° + 45° > 60°
D. 4 + 8 > 15, 8 + 15 > 4, 4 + 15 > 8
Therefore, all of the measurements could create more than one triangle.